A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In order to accurately position the patterning device relative to the substrate, stage apparatuses equipped with one ore more electromagnetic motors are often applied.
In general, such an electromagnetic motor includes a first part including one or more coils which can be supplied with an electrical current and a second part co-operating with the first part to generate, in use, a force between both parts. The second part may e.g. include a 1D or 2D array of permanent magnets which generates an alternating magnetic field in a given direction or a given plane, the magnetic field interacting with the current carrying coils of the first part to generate the force between both parts.
It is known that an electromagnetic motor which is used to position an object, e.g. a substrate table in a lithographic apparatus, may generate both a primary force, i.e. a force in a given direction to position the object, and, at the same time, produce a parasitic effect such as a pitch torque. Such a phenomenon is adequately described for a planar motor in e.g. EP 1 357 434 which is incorporated herein by reference in its entirety.
Due to the pitch torque, the accurate positioning of the object may be compromised; the occurrence of the pitch torque may affect the positioning of the object that is to be positioned, even when the object is not directly coupled to the electromagnetic motor, e.g. by cross-talk between the electromagnetic motor and a fine positioning stage mounted between the object and the electromagnetic motor. Although the cross-talk to such a fine positioning stage may be low, there will always be, to some extend, a transmission of forces due to e.g. cables or hoses from the motor to the fine positioning stage, thereby affection the positioning of the object.
Due to the pitch torque, the relative position between both parts that constitute the electromagnetic motor may change. In general, both parts are kept apart by either a type of bearing such as an air bearing or, the motor itself may generate the required forces for maintaining a predetermined or preferred or minimum distance between both motor parts. The occurrence of the pitch torque may disturb this to such extend that both motor parts may even come in contact with each other. This may, apart from resulting in a positioning error for the object, result in damaging either or both parts of the motor or result in contamination of the area in which the motor operates. A solution to avoid such a collision between both motor parts is to increase the distance between both parts. The skilled person will however appreciate that this would result in a reduced efficiency of the motor, since an increased distance between both parts will diminish the magnetic coupling between both parts. Apart from the reduction in efficiency, it will be clear that this approach will not satisfactory solve the occurrence of the positioning error due to the pitch torque. It is therefore suggested in EP 1 357 434 to use a modified controller to generated the required motor forces, the modified controller being arranged such that the effect of the pitch torque is substantially reduced. However, this may require an important amount of calculating power. The methods as suggested may be difficult to implement in a digital controller because the required calculations would be difficult to achieve within one sample of the controller. Delaying the output of the controller, i.e. using several samples to conduct the calculations, may affect the stability of the control loop or the positional accuracy obtained.